$A$ particle of mass $m$ moves in a circle of radius $r$. Its centripetal acceleration changes with time according to the formula $a_c = k^2 r t^2$. What is the power delivered to the particle by the force acting on it?

In non-uniform circular motion,the ratio of tangential to radial acceleration is ($r$ is the radius of the circle,$v$ is the speed of the particle,$\alpha$ is the angular acceleration).

$A$ point $P$ moves in a counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^3 + 5$,where $s$ is in meters and $t$ is in seconds. The radius of the path is $20 \ m$. The acceleration of $P$ when $t = 2 \ s$ is nearly .......... $m/s^2$.

For a particle in a uniformly accelerated circular motion:

For a particle in a non-uniform accelerated circular motion:

$A$ car moves with a speed of $30 \, m/s$ on a circular path of radius $500 \, m$. If its tangential acceleration is $2 \, m/s^2$,what is the magnitude of the total acceleration of the car in $m/s^2$?